 line passes through the given points. Note that the y-intercept is not given. Find m and b and write the linear rule. A graph may be helpful.
a (-1, 1) and (1, 5)

To find the linear equation of a line passing through two points, we need to determine the **slope (m)** and the **y-intercept (b)**. The general form of a linear equation is:

\[
y = mx + b
\]

### Step 1: Find the slope (m)

The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Where:
- \( (x_1, y_1) = (-1, 1) \)
- \( (x_2, y_2) = (1, 5) \)

Now, substitute the points into the formula:

\[
m = \frac{5 - 1}{1 - (-1)} = \frac{4}{2} = 2
\]

So, the slope \( m = 2 \).

### Step 2: Find the y-intercept (b)

We now use one of the points and the slope to find the y-intercept \( b \). Using the point-slope form \( y = mx + b \), substitute the slope and the coordinates of one of the points, say \( (-1, 1) \).

\[
1 = 2(-1) + b
\]

Solve for \( b \):

\[
1 = -2 + b
\]
\[
b = 3
\]

### Step 3: Write the linear equation

Now that we know the slope \( m = 2 \) and the y-intercept \( b = 3 \), the linear equation of the line is:

\[
y = 2x + 3
\]

This is the required equation of the line.

Would you like to see a graphical representation of this line? Let me know if you'd like more details or have any questions.

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Here are 5 related questions for further practice:
1. What is the equation of a line passing through the points \( (2, 4) \) and \( (6, 12) \)?
2. How do you determine the slope of a horizontal line?
3. If a line has a slope of 0, what can you say about its graph?
4. Find the equation of a line with a slope of 3 and passing through the point \( (0, 2) \).
5. How do you find the equation of a line parallel to \( y = 2x + 3 \) but passing through \( (3, 1) \)?

**Tip:** When calculating slope, always be careful with the signs of the coordinates!

Line passes through the given points. Note that the y-intercept is not given. Find m and b and write the linear rule. A graph may be helpful. Points: (-1, 1) and (1, 5).

Learn how to find the linear equation of a line passing through points (-1, 1) and (1, 5). This problem explains the calculation of slope (m = 2) and y-intercept (b = 3) using key algebraic concepts. Suitable for students in Grades 8-10.

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